//Standard generators of S6(2) are a and b where a is in class 2A, b has order 7
//and ab has order 9.  Standard generators of the double cover 2.S6(2) are
//preimages A and B where B has order 7 and AB has order 9.  
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ ];
//irreducible

_LR`G := sub<GL(15,Integers()) |
\[ 0,0,0,0,1,-1,0,0,0,0,-1,0,-1,-1,1,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,-1,0,0,0,0,0,1,
-1,1,0,0,0,-1,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,-1,0,1,
-1,0,0,0,0,0,1,0,0,0,1,0,-1,0,1,0,-1,0,0,0,-1,1,0,-1,
0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
-1,0,-1,0,0,-1,0,0,-1,1,0,-1,0,0,1,0,-1,1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,-1,0,1,0,0,-1,0,0,
-1,0,0,0,-1,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0 ],
\[ 0,0,0,1,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,
1,-1,0,-1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,-1,-1,1,0,0,1,-1,-1,1,0,0,0,0,1,0,1,
0,0,-1,0,1,0,-1,1,0,0,0,0,1,0,0,0,0,0,0,1,-1,0,1,-1,
0,0,0,0,0,1,0,0,0,1,0,-1,0,1,-1,0,0,0,0,0,1,0,-1,0,
0,0,-1,-1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,-1,0,
0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,1,0,-1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1 ] >;

return _LR;
